Abstract
We propose and validate a framework for analog simulation of the Heisenberg spin model using a circuit quantum electrodynamics (circuit-QED) platform. Our method involves the Dyson-Maleev transformation, for which we develop a procedure to circumvent its inherent non-Hermiticity, yielding the extended Bose-Hubbard (EBH) Hamiltonian. We demonstrate the equivalence of this approach to the Holstein-Primakoff encoding for spin-1/2 systems. For the experimental realization of this EBH model, we design a scalable circuit-QED architecture based on an engineered Josephson junction array. Numerical simulations confirm that the microwave photon dynamics in this simulator accurately reproduces the original spin dynamics. Our work establishes an experimentally accessible method for investigating complex quantum spin dynamics in a highly controllable bosonic setting.
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